Random pulse generator

ABSTRACT

A system for generating electronic pulses separated by intervals which vary according to a predetermined probability distribution, typically exponential. The predetermined probability distribution is realized through the interaction of two other separately controlled functions. A first probability function statistically governs the selection of a first value and a second time varying function establishes the pulse time interval by relation to the selected first value.

[ RANDOM PULSE GENERATOR [75] Inventor: Herbert E. Miller, Brookline,Mass.

[73] Assignee: Epsco Incorporated, Westwood,

Mass.

221 Filed: July 14,1972

[21] Appl. No.: 211,704

[ Sept. 11, 1973 Primary Examiner -John Komins lt i Attorney-JosephWeingarten Stanley M. Schurgin etal.

[57] ABSTRACT A system for generating electronic pulses separated byintervals which vary according to a predetermined probabilitydistribution, typically exponential. The predetermined probabilitydistribution is realized through 328/158 the interaction of two otherseparately controlled funcle 0 e R tions. A first probability functionstatistically governs Reerences Cited the selection of a first value anda second time vary ng function establishes the pulse time interval byrelation UNITED STATES PATENTS to the selected first value.

3,573,652 4/l97l Charters 331/78 8 Claims, 3 Drawing Figures Digital 20Random Digitol z Ref Generator Converter 1 Offs" 26 I 24 I2 PulseExponetiol Deloy c 2:9: Decoy compormor Multivibrctor on Generator FineFeed back Adjust Control Value Output -0 PATENTED l [975 3.758.873

SHEET 1 0F 2 FIG. l l6 l4 Di ital Random 9 Digital Analog Ref GeneTmmrConverter offse' 26 24 l 2 Pulse Exponetiul fly omput ifi c3312. $2132:6

enero or Fine Feedback Adjust Control Value Output 2 A A(t) 3O AMAX FIG.2

A0 MAX A 2*. A(t)=Amc|xexp RANDOM PULSE GENERATOR FIELD OF THE INVENTIONThis invention relates to pulse generators and in particular'to a randompulse generator for providing a sequence of pulses at intervals whichare statistically governed by a decaying exponential probabilitydistribution.

BACKGROUND OF THE INVENTION While a sequence of electrical signals mayappear to have a random occurrence, a sufficiently large sample of thepulse sequence, particularly if it is ergotic, can be statisticallyanalyzed to determine the distribution of pulse intervals and therebydefine the pulse sequence according to its probability distribution.This statistical proposition pennits one pulse sequence having oneprobability distribution to be distinguished from another pulse sequencewith a different probability distribution.

Systems employing this statistical theory commonly require thegeneration of a pulse sequence where the pulse interval is governed byan established probability distribution, typically an exponential decay.Generators of this sort are known and have commonly included a noisegenerator for producing a random amplitude signal and a comparator fordetecting each traversal of a preset threshold level by the randomamplitude signal. Each detected traversal results in the generation of apulse and over time a sequence of pulses is produced with approximatelythe desired exponential distribution. In addition to the theoreticalinaccuracy of this technique a further drawback is the difficulty ofaccurately controlling the average pulse rate determined by the level ofthe threshold. This difficulty may be due to temperature sensitivity inthe threshold comparison system as well as interference from othersources where the interference has a probability distribution distinctfrom that of the generated noise. Frequency demands are also placed onthe noise generator to provide the necessary wideband noise signal.

BRIEF SUMMARY OF THE PREFERRED EMBODIMENT In a preferred embodiment forapplicant's invention on the other hand two predetermined signal leveldistributions interact in a manner that provides a real time sequence ofpulses at intervals governed by a desired probability distribution. Theuse of two separately controllable signal level distributions to producethe desired interval probability provides a more accurate and flexiblerandom pulse generator.

While many distributions are possible, in a specific example for thepresent invention the pulse interval is to be governed by an exponentialdecay distribution. A random amplitude generator is provided to producea constant signal amplitude in response to a trigger signal. Theprobability for the generation of all amplitude levels is equal, makingthe probability distribution a constant. The trigger signal alsoinitiates an exponential decay signal from a further generator and therandomly generated constant amplitude and decaying amplitude signals areapplied to a comparator to detect equality therebetween. Detectedequality causes the generation of each pulse in the sequence and alsoproduces the trigger signal which causes the process to be repeated forthe production of the sequence of output pulses.

To provide accurate control over the average interval between pulses, afeedback circuit is provided to detect the average interval and toadjust the exponential decay rate so as to maintain a preselectedaverage pulse interval.

DESCRIPTION OF THE DRAWINGS These and other features of the inventioncan be more fully understood from. the detailed description of apreferred embodiment presented below for purposes of illustration, andnot by way of limitation, and from the accompanying drawings of which:

FIG. 1 is a block diagram "of a system according to the invention;

FIG. 2 is a probability distribution chart useful in understanding theinvention; and

FIG. 3 is a schematic diagram of a random pulse generator according tothe invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT With reference to FIG.1 the basic principles of operation of the generator according to theinvention to provide an exponential decay distribution can be seen toreside in comparing the output of a random signal generator with theoutput of an exponential decay generator. To this end, a comparator 12receives an analog signal from a digital-to-analog converter 14 whichresponds to the digital signals of a random digital signal generator 16.The generator 16 responds to a reset signal to produce a random digitalnumber which in turn is converted to a random amplitude level byconverter 14. The probabilities of occurrence for all random digitalnumbers within a range are equal thus providing a constant probabilitydistribution for the amplitude output of converter 14 within thecorresponding range. The comparator 12 also responds to an exponentialdecay signal from a generator 18. The exponential decay signal'isreinitiated in response to each occurrence of a reset signal. Thecomparator 12 may be provided with a predetermined offset from areference offset 20 for purposes to be explained below. The comparatorl2 detects the equality between its inputs from the converter 14 andgenerator 18. The detected equality triggers a delay multivibrator 22commonly called a one-shot circuit to produce the pulse output. Thedelay multivibrator 22 is operative to respond only to one slope in theoutput from comparator 12 so that the pulse is generated only duringdecay portions of the generator 18 and not reset portions.

The reset signals for the generators 16 and 18 are provided from themultivibrator pulse output and in the case of the random digitalgenerator 16 causes the generation of a new, random digital signal. Thereset signal in the case of the exponential decay generator 18reinstates the exponential decay from a predetermined initial level.This initial level is chosen to be greater than the largest magnitudepossible at the output of the digital-to-analog converter 14 to insurethat the exponential decay will always start from above the constantamplitude signal. For similar reasons, the offset reference 20 isprovided to the comparator 12 to insure that the exponential decay will,in a finite time, traverse the lowest possible level from thedigital-to-analog converter 14. An optional approach is to cause thedigitalto-analog converter 14 to respond to only the most significantbits from the random digital generator 16 leaving one or more leastsignificant bits to define a predetermined minimum value for the outputof the con verter 14.

The average pulse interval is selectable by a rate control 24 inresponse to a selector 26. A coarse rate adjust signal is appliedtherefrom to the exponential decay generator 18 while a finer resolutionrate control signal is applied to a feedback controller 28. The feedbackcontroller 28 also responds to the pulse output from the multivibrator22 to compare the selected average interval to a detected actual averageinterval and to provide a feedback adjustment to the exponential decaygenerator 18 to produce a change in decay rate and correspondingly aregulation of the average pulse interval to the selected length.

By reference to FIG. 2 the interraction of two signal leveldistributions to produce the ultimately desired randomness in the outputpulse interval can be more fully understood. in FIG. 2, a graph 30corresponds to the probability function governing the signal amplitudefrom the converter 14 while a graph 32 indicates the exponential decaysignal level variation with time which is provided by the exponentialdecay generator 18. These two graphs 30 and 32 are placed adjacent toeach other so that each has in common a vertical axis representingamplitude as applied to the comparator 12. The exponential decay graph32 has the right hand horizontal axis represent time, and the randomsignal level graph 30 has its left hand horizontal axis representprobability of occurrence of the amplitudes from the converter 14.

The coaction of the curves 30 and 32 to result in the probabilityfunction 34 can be expressed mathematically using known statisticaltheory, see for example A. Papoulis, Probability, Random Variables, andStochastic Processes, McGraw Hill, 1965, p. 126 et seq. In the generalcase for a curve like 32, A and t are related by the function in therange A, to A, AA where AA is determined from At at t, by therelationship A A(t) in the limit where At becomes dt and AA becomes dA,the probability, f, (t)dt, of t being between t, and t, dt is the sameas the probability, f (A) ldA of A being betweenA and A,,+AA, or

' then,

110( f..(A) m" r he d f,,,(A) is determined from the known probabilityfunction represented by curve 30 and ldt/dA, I is found from the secondfunction A A(t) represented by curve 32.

Equations (l), (2), and (3) indicate the manner in which two signallevel distributions, f ,(A) and A(t), the functions governing theoperation of generators 16 and 18 respectively, coact to produce theresultant output interval probability distribution, in this case anexponential decay function. These equations also indicate theflexibility of the system in producing a variety of desired outputinterval distributions by permitting adjustment of the generators l6 and18 to achieve that result. For example, if a constant distribution isdesired within a predetermined interval range, the generator 18 can bedesigned to provide a constant slope ramp.

It can be now appreciated that pulse interval probability distributionswhich are difficult or impossible to realize in a random pulse generatorof conventional design may, according to the implementation of thepresent invention, be more simply and accurately realized as thecoaction of two separate functions. While the ultimately desiredprobability distribution provides a restraint on the generator output,the two separate functions utilized to produce the ultimate distributionare not in general uniquely restrained and several different sets of thetwo functions may be employed. The random pulse generator designer maythus not only choose a set which can be practically implementedelectronically, but one which satisfies accuracy or other conditions forthe ultimate distribution. Moreover, complex distributions may beimplemented by, for example, a multiple root function for generator 18such as a damped sinusoid. Additionally while the ultimate probabilitydistribution of the present implementation governs a pulse interval, theinvention may also be employed to generate values other than time forthe ultimately desired distribution as for example by using a time tosignal level converter 29.

To more specifically indicate the design of the generator to accomplishthis exponential decay distribution for the pulse intervals, referenceis made to FIG. 3. The constant probability distribution for a boundeddigital magnitude as provided by the generator 16 is shown in FIG. 3 asbeing produced by a 16 bit shift register 36 which receives at its inputthe bit output of a Modulo 2 adder 38. Modulo 2 adders are known in theart and essentially operate to produce a binary one output if the numberof binary 1 inputs is odd. To provide randomness in the digital contentsof the register 36 the Modulo 2 adder 38 responds to the digital statesof the fourth, thirteenth, fifteenth, and sixteenth bits of shiftregister 36. The register 36 shifts in the signal from the adder 38 andshifts each bit one position in response to a clock input from a clockbuffer 40. A digital-toanalog converter 42 responds to the 12 mostsignificant bits in the 16 bit shift register 36 to provide acorresponding analog output signal for application to a comparator, highgain differential amplifier 44. The digitalto-analog converter 42receives a reference input from a voltage source 46.

The exponential decay is provided under the control of an average rateselector switch system 48 which provides a multi-bit digital output to abinary rate multiplier 50. The selected average rate can typically rangefrom zero to ten thousand pulses per second. The binary rate multiplierresponds to a predetermined high impulse rate from stable oscillator 52to produce an output pulse rate having an average interval specified bythe selection in the switch system 48 as is known in the art. Thisselected average rate pulse stream is supplied from the binary ratemultiplier 50 to an up-down counter 54 on a count-up input. Oscillator52 provides the systm time reference and accordingly its stability isdefined by required system time accuracy.

The binary rate selector output is also applied to a coarse range logiccircuit 56 which may be a series of gates for detecting in which of fourpredetermined portions of the range of selectable average rates is theselected rate. The logic 56 has three outputs corresponding to all butone portion of the range and these are respectively applied to the basesof grounded-emitter NPN transistors 58, 60 and 62. The collectors ofthese transistors are respectively biased through sources 64, 66 and 68and are further connected to respective capacitors 70, 72 and 74.Opposite terminals of the capacitors 70, 72 and 74 are joined in commonto a capacitor 75 which is permanently grounded and the common point isapplied to a differential noninverting input of the high gain comparisonamplifier 44.

According to the range for the selected average rate, one or more of thecapacitors 70, 72 and 74 is enabled for charging through itscorresponding transistor. Charging is provided by' current through theemittercollector circuit of a PNP transistor76 from a source 78coincident with each pulse output as will be explained. Capacitor 75 ispermanently connected for charging with each pulse to establish thefourth range portion. Discharging of the one or more charging capacitorsis through one or more of a plurality of resistors 80, 82, 84 and 86,also connected to the noninverting input of the comparison amplifier 44.These resistors are selectively grounded through grounded-emitter NPNtransistors 88, 90, 92 and 94. Transistors 88, 90, 92 and 94 may beoperated in the grounded collector mode for better switching The basesof these transistors 88, 90, 92 and 94 are controlled by a butteramplifier system 96 which responds to respective digital states of theup-down counter 54. While only four stages of resistor and transistordischarge circuits for the capacitors 70, 72 and 74 have been shown itis to be understood that a greater number may be used depending upon theaccuracy desired in the fine control of the average pulse interval.

At the point where the decaying signal applied to the noninverting inputof the amplifier 44 reaches the level of the constant input applied fromthe converter 42 to the inverting input of the amplifier 44, theamplifier 44 rapidly changes its output from a high to a low value andthis negative slope transition triggers a delay multivibrator 98 togenerate an output pulse. The resulting pulse is applied to the clockbuffer 40 to provide the clock signal to the shift register 36 causingit to cycle one bit and assume a new random number and is also appliedto a buffer amplifier 100 for driving the base of the PNP chargingtransistor 76 for a sufficient duration to charge one or more of thecapacitors 70, 72, 74 and 75 to the voltage of the source 78. The pulseoutput from the multivibrator 98 is also applied to a countdown input ofthe counter 54 and causes the digital magnitude therein to decrease onebit.

The resulting control over the discharge rate through the resistors 80,82, 84 and 86 by the counter 54 results in regulation of the averagepulse interval to the rate selected by the switch system 48. Thus if theaverage rate is too low the counter 54 will increase its count andcorrespondingly increase the discharge rate through resistors 80, 82, 84and 86 to reduce the average pulse interval until equilibrium isachieved. The resistors 80, 82, 84 and 86 increase in resistance by afactor of two, the greatest resistance corresponding to the leastsignificant bit in the counter 54. v

To insure that the exponential decay signal applied to the noninvertinginput of the amplifier 44 will traverse all possible digital magnitudesapplied in analog form to the inverting input, the reference voltage 78is made slightly larger than the reference voltage 46. This insures thatthe initial value for the exponential decay will be larger than thehighest value that the digital-to- ,analog converter 42 is capable ofproducing. Similarly,

a high value resistor 102 is connected to a negative source 104 from thenoninverting input of the amplifier 44 to insure that the exponentialdecay traverses the lowest possible signal level from the converter 42,in this case by ultimately becoming negative.

In order to insure that the shift register 36, operating in a feedbackloop through the modulo 2 adder 38, produces a random state, a tum-onjam signal 106 is applied to the register 36 to insure at least one highlevel bit is contained in the register at tum-on.

As can be seen from the detailed description in FIG. 3, the random pulsegenerator provides a simple and easily controlled means of generating arandom pulse signal with an exponential decay distribution to the pulseintervals without the need for employinga noise or other erratic, andcontinuously operating, signal source. A feedback control systemprovides precise regulation of the average pulse rate to a predeterminedaverage rate. It can also be appreciated by those skilled in the artthat instead of the constant probability distribution provided by theshift register 36 a number of other distributions, implemented by knowndigital techniques, can be employed to achieve a differentdistribution,f ,(A), for use in the system. Similarly, different analogor digital implementations of the decay or, optionally, increasingsignal used for comparison purposes can be implemented and according tothe equations indicated above will produce a different probabilitydistribution for the output pulse interval.

It will thus occur to those skilled in the art that alterations andmodifications can be made to the specific probability functions as wellas circ'uitry employed in the invention depending upon their individualrequirements. It is accordingly intended to limit the scope of theinvention only as indicated in the following claims.

What is claimed is:

l. A system for producing a sequence of values with each value governedby a predetermined probability, said system comprising:

means for repeatedly selecting a signal level from within a range ofsignal levels according to a preset probability function;

means for providing a transformation between a first range of signalvalues and a second range of signal values whereby each signal value insaid first range produces one or more corresponding signal values insaid second range;

means responsive to each selected signal level and operativelyassociated with said transformation providing means for detecting fromsaid transformation providing means a signal value in said second rangecorresponding to the signal value in said first range represented byeach said selected signal level;

a plurality of said output signal values from repeated selections of oneof said signal levels providing said sequence of values according to thepredetermined probability;

said predetermined probability being determined by coaction of thefunctions describing the selections of said signal level selecting meansand the transformations of said transformation providing means.

2. The system of claim 1 wherein:

said transformation providing means includes means for generating thevalues in said first range as a function of time within said secondrange;

said detecting means includes means for comparing said values in saidfirst range with said selected signal level to determine equalitytherebetween; and

means responsive to a determination of equality for providing a timeinterval corresponding to the time represented by said generating meansat said determined equality.

3. The system of claim 1 wherein said signal level selecting meansincludes:

a random signal generator; and

means for providing each random signal over a range extending withinsaid first range of values.

4. The system of claim 1 further including:

means for selecting an average value for said sequence of values; and

means responsive to the selected average value and said plurality ofoutput values for regulating the average value of the output valuesdetected from said transformation providing means.

5. The systemof claim 1 wherein said transformation providing meansincludes means for providing a plurality of signal values in said secondrange corresponding to the signal value in said first range representingthe signal level selected.

6. A pulse generator for producing a sequence of electrical outputpulses at intervals governed by a predetermined probabilitydistribution, said pulse generator comprising:

means responsive to a first signal for producing a signal amplitudewithin a range of amplitudes, said produced signal amplitude beinggoverned by a predetermined probability function;

means operative in response to said first signal for generating apredetermined signal waveform as a function of time;

means for comparing said produced signal amplitude and said generatedsignal waveform and operative to produce a timing signal in response toa predetermined coincidence between said produced signal amplitude andsaid predetermined waveform;

means operative in response to said timing signal for producing one ofsaid sequence of output pulses; and

means further operative in response to said timing signal for producingsaid first signal for application respectively to said signal amplitudeproducing means and said signal waveform generating means to providerecycling thereof in order to permit production of a sequence of outputpulses.

7. The pulse generator of claim 6 further including:

means responsive to said sequence of output pulses for providing asignal representative of the actual average interval between pulses inthe pulse output sequence;

means for providing selection of an average interval between pulses; and

means for adjusting said predetermined waveform signal generating meansin response to the selected average interval and the actual averageinterval signal to cause said actual average interval between pulses toapproach said selected average interval.

8. A pulse generator for producing output pulses at intervals varyingaccording to a predetermined probability distribution, said generatorincluding:

a shift register operative to shift digital signals therein in responseto a clock signal;

means for applying a digital input to said shift register as apredetermined combination of a plurality of the binary states of saidshift register;

means for converting the binary states of said shift register to ananalog signal representing the magnitude of said binary states;

means for selecting an average pulse interval;

means operative in response to said selected average pulse interval forproducing a pulse sequence at a corresponding pulse rate;

a plurality of capacitors;

a plurality of resistors operative to discharge said plurality ofcapacitors;

means for charging said plurality of capacitors to a predeterminedsignal level in response to an output pulse;

means operative in response to predetermined ranges in said selectedaverage pulse interval for selectively connecting said plurality ofcapacitors for discharge through said plurality of resistors;

means for accummulating a digital representation of the difference inrate of pulse occurrence between pulses in said pulse sequence and saidoutput pulses; v

means operative in response to each bit of said digital representationfor selectively enabling a corresponding one of said plurality ofresistors as a discharge path for said plurality of capacitors;

means responsive to said first signal for generating said clock signalfor said shift register;

means for comparing the voltage level of said plurality of capacitorsduring discharge by said plurality of resistors with said analog signalto produce a comparison signal in response to detection of apredetermined relation therebetween; and

means for producing one of said output pulses in response to each saidcomparison signal.

1. A system for producing a sequence of values with each value governedby a predetermined probability, said system comprising: means forrepeatedly selecting a signal level from within a range of signal levelsaccording to a preset probability function; means for providing atransformation between a first range of signal values and a second rangeof signal values whereby each signal value in said first range producesone or more corresponding signal values in said second range; meansresponsive to each selected signal level and operatively associated withsaid transformation providing means for detecting from saidtransformation providing means a signal value in said second rangecorresponding to the signal value in said first range represented byeach said selected signal level; a plurality of said output signalvalues from repeated selections of one of said signal levels providingsaid sequence of values according to the predetermined probability; saidpredetermined probability being determined by coaction of the functionsdescribing the selections of said signal level selecting means and thetransformations of said transformation providing means.
 2. The system ofclaim 1 wherein: said transformation providing means includes means forgenerating the values in said first range as a function of time withinsaid second range; said detecting means includes means for comparingsaid values in said first range with said selected signal level todetermine equality therebetween; and means responsive to a determinationof equality for providing a time interval corresponding to the timerepresented by said generating means at said determined equality.
 3. Thesystem of claim 1 wherein said signal level selecting means includes: arandom signal generator; and means for providing each random signal overa range extending within said first range of values.
 4. The system ofclaim 1 further including: means for selecting an average value for saidsequence of values; and means responsive to the selected average valueand said plurality of output values for regulating the average value ofthe output values detected from said transformation providing means. 5.The system of claim 1 wherein said transformation providing meansincludes means for providing a plurality of signal values in said secondrange corresponding to the signal value in said first range representingthe signal level selected.
 6. A pulse generator for producing a sequenceof electrical output pulses at intervals governed by a predeterminedprobability distribution, said pulse generator comprising: meansresponsive to a first signal for producing a signal amplitude within arange of amplitudes, said produced signal amplitude being governed by apredetermined probability function; means operative in response to saidfirst signal for generating a predetermined signal waveform as afunction of time; means for comparing said produced signal amplitude andsaid generated signal waveform and operative to produce a timing signalin response to a predetermined coincidence between said produced signalamplitude and said predetermined waveform; means operative in responseto said timing signal for producing one of said sequence of outputpulses; and means further operative in response to said timing signalfor producing said first signal for application respectively to saidsignal amplitude producing means and said signal waveform generatingmeans to provide recycling thereof in order to permit production of asequence of output pulses.
 7. The pulse generator of claim 6 furtherincluding: means responsive to said sequence of Output pulses forproviding a signal representative of the actual average interval betweenpulses in the pulse output sequence; means for providing selection of anaverage interval between pulses; and means for adjusting saidpredetermined waveform signal generating means in response to theselected average interval and the actual average interval signal tocause said actual average interval between pulses to approach saidselected average interval.
 8. A pulse generator for producing outputpulses at intervals varying according to a predetermined probabilitydistribution, said generator including: a shift register operative toshift digital signals therein in response to a clock signal; means forapplying a digital input to said shift register as a predeterminedcombination of a plurality of the binary states of said shift register;means for converting the binary states of said shift register to ananalog signal representing the magnitude of said binary states; meansfor selecting an average pulse interval; means operative in response tosaid selected average pulse interval for producing a pulse sequence at acorresponding pulse rate; a plurality of capacitors; a plurality ofresistors operative to discharge said plurality of capacitors; means forcharging said plurality of capacitors to a predetermined signal level inresponse to an output pulse; means operative in response topredetermined ranges in said selected average pulse interval forselectively connecting said plurality of capacitors for dischargethrough said plurality of resistors; means for accummulating a digitalrepresentation of the difference in rate of pulse occurrence betweenpulses in said pulse sequence and said output pulses; means operative inresponse to each bit of said digital representation for selectivelyenabling a corresponding one of said plurality of resistors as adischarge path for said plurality of capacitors; means responsive tosaid first signal for generating said clock signal for said shiftregister; means for comparing the voltage level of said plurality ofcapacitors during discharge by said plurality of resistors with saidanalog signal to produce a comparison signal in response to detection ofa predetermined relation therebetween; and means for producing one ofsaid output pulses in response to each said comparison signal.